Global modes constituting the solar magnetic cycle. II - Phases, 'geometrical eigenmodes', and coupling of field behaviour in different latitudes

Abstract

We show that the axisymmetric odd degree SHF modes of 21.4-yr periodicity and degrees l le 29 in the solar magnetic field (as inferred from sunspot data during 1874–1976), are at least approximately stationary. Among the sine and cosine components of these SHF modes we find four groups, each defining the geometry of a coherent global oscillation characterized by a distinct power hump and its own level of variation. The first two of these lsquogeometrical eigenmodesrsquo (viz., B 1 and B 2), define the large-scale structure of the butterfly diagrams. Remaining SHF modes define the orderliness of the field distribution even within the lsquowingsrsquo of the lsquobutterfliesrsquo down to scales l ap 29. These include the lsquogeometrical eigenmodesrsquo B 3 and B 4, which are not present in simulated data sets in which the latitudes of the sunspot groups are randomly redistributed within the lsquowingsrsquo of the lsquobutterfliesrsquo. Superposition of B 1, B 2, B 3, and B 4 is necessary and sufficient to reproduce important observed properties of the latitude-time distribution of the real field, not only in the lsquosunspot zonersquo, but also in the middle (35°–75°) and the high (gap75°) latitudes, with appropriate relative orders of magnitude and phases. Thus, B 1, B 2, B 3, and B 4 seem to represent really existing global oscillations in the Sun's internal magnetic field. The geometrical form of B 1 may also be the form of the lsquoforcingrsquo oscillation.